Table 1 Minimum and maximum values of \(\text {V}^{\text {unif}}_{s}\) and values for the equal spacing model \(\tilde{\text {V}}^{\text {unif}}_{s}\), for \(\alpha =0.5\) for early (\(t_{1}\)), mid (\(t_{2}\)) and late (\(t_{3}\)) interim analyses, where \(\tau \text {0}_{1}=0.15\), \(\tau \text {0}_{2}=0.30\) and \(\tau \text {0}_{3}=0.45\) respectively, for s from two to six for the fixed, increasing and decreasing rate recruitment models. Also shown are values of \(\text {D}=(1-\alpha )(1+(s-1)\alpha )/(1+(s-2)\alpha )\) and \(n_{s1}\) for each setting

[a] Fixed

 2

0.75

0.55

-

0.89-0.89

0.71

-

0.93-0.93

0.78

-

0.95-0.95

 3

0.67

0.55

0.86

0.85-0.89

0.71

0.91

0.90-0.93

0.78

0.94

0.93-0.95

 4

0.62

0.55

0.85

0.83-0.89

0.71

0.90

0.89-0.93

0.78

0.93

0.92-0.95

 5

0.60

0.55

0.84

0.82-0.89

0.71

0.90

0.88-0.93

0.78

0.92

0.91-0.95

 6

0.58

0.55

0.83

0.81-0.89

0.71

0.89

0.88-0.93

0.78

0.92

0.91-0.95

[b] Increasing

 2

0.75

0.59

-

0.90-0.90

0.68

-

0.92-0.92

0.72

-

0.93-0.93

 3

0.67

0.59

0.88

0.86-0.90

0.68

0.90

0.89-0.92

0.72

0.92

0.91-0.93

 4

0.62

0.59

0.86

0.84-0.90

0.68

0.89

0.88-0.92

0.72

0.91

0.90-0.93

 5

0.60

0.59

0.85

0.83-0.90

0.68

0.89

0.87-0.92

0.72

0.90

0.89-0.93

 6

0.58

0.59

0.85

0.83-0.90

0.68

0.88

0.87-0.92

0.72

0.90

0.88-0.93

[c] Decreasing

 2

0.75

0.42

-

0.86-0.86

0.62

-

0.91-0.91

0.74

-

0.93-0.93

 3

0.67

0.42

0.82

0.81-0.86

0.62

0.88

0.87-0.91

0.74

0.92

0.91-0.93

 4

0.62

0.42

0.80

0.78-0.86

0.62

0.87

0.86-0.91

0.74

0.91

0.90-0.93

 5

0.60

0.42

0.79

0.77-0.86

0.62

0.86

0.85-0.91

0.74

0.91

0.89-0.93

 6

0.58

0.42

0.78

0.76-0.86

0.62

0.86

0.84-0.91

0.74

0.90

0.89-0.93